Can thinking happen at some other time than the moment? Just don't let thinking distract you too much from experiencing the moment. You really don't need to think that often...spend most of your time out of your head and in your body...100% devoted to the experience you are having right now.

But there really is only so much attention to spread between thinking and experiencing...so if you are fully in the moment, there is no thought.
Can you mix thinking and experiencing...of course. I don't recommend it for the normal mode of living. Thought is a vice and bad habit. We do far more than is really needed.

When thinking is needed though...it is done in the now. Everything that happens is in the now.